Squeezed in three dimensions, moving in two: Hydrodynamic theory of 3D incompressible easy-plane polar active fluids

TL;DR

This paper develops a hydrodynamic theory for 3D incompressible polar active fluids with easy-plane symmetry, revealing their universality class and calculating velocity correlations.

Contribution

It establishes the universality class of 3D easy-plane polar active fluids and maps their behavior onto known equilibrium systems, providing new theoretical insights.

Findings

Hydrodynamic model belongs to the same universality class as a 3D anisotropic magnet.

The model maps onto a DNA-lipid mixture in the sliding columnar phase.

Divergent renormalization of damping coefficients and velocity correlation functions are obtained.

Abstract

We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible polar active fluids. We show that the hydrodynamic model for this system belongs to the same universality class as that of an equilibrium system, namely a special 3D anisotropic magnet. The latter can be further mapped onto yet another equilibrium system, a DNA-lipid mixture in the sliding columnar phase. Through these connections we find a divergent renormalization of the damping coefficients in 3D easy-plane incompressible polar active fluids, and obtain their equal-time velocity correlation functions.